a robust numerical method for multi-asset option pricing

In this work, we numerically solve a multi-asset european call option withthe finite difference method (fdm) and take the advantages of the antithetic montecarlo simulation as a variance reduction technique in the end point of the domain, andthe linear boundary condition has been implemented in other boundaries. we also apply the grid stretching transformation to make a non-equidistance discretization withmore nodal points around the strike price which is the non-smooth point in the payofffunction to reduce the numerical errors around this point and have more accurate results. superiority of our method (gsmcbc) will be demonstrated by comparison withthe standard finite difference scheme with the equidistance discretization and the linearboundary conditions (lbc) and also combination of the lbc scheme with the standardmonte carlo simulation at the end point of the domain (mcbc). furthermore, the rootmean square errors (rmse) of these three schemes in the most interesting region whichis around the strike price, have been compared.